论文标题
对数线性动态反演控制，并具有可证明的安全保证在谎言组中
Log-linear Dynamic Inversion Control with Provable Safety Guarantees in Lie Groups
论文作者
论文摘要
在本文中，我们使用指数映射的派生型来得出混合不变系统的跟踪误差对数的确切演变，这是一类能够描述Lie组中刚性身体跟踪问题的系统。此外，我们设计了基于对数线性动力反演的对照法律，以消除由于空间曲率而导致的非线性并增强控制器的鲁棒性。我们应用线性矩阵不等式（LMI）来绑定跟踪误差，如果有界的干扰矩阵放大的有界干扰，并利用绑定以创建流量管道的跟踪误差。为了证明我们方法的有用性，我们使用简化的运动学飞机模型和基于多项式的路径计划方法来展示其使用城市空气移动性（UAM）方案的应用。
In this paper, we use the derivative of the exponential map to derive the exact evolution of the logarithm of the tracking error for mixed-invariant systems, a class of systems capable of describing rigid body tracking problems in Lie groups. Additionally, we design a log-linear dynamic inversion-based control law to remove the nonlinearities due to spatial curvature and enhance the robustness of the controller. We apply Linear Matrix Inequalities (LMIs) to bound the tracking error given a bounded disturbance amplified by the distortion matrix and leverage the tracking error bound to create flow pipes. To demonstrate the usefulness of our method, we show its application with Urban Air Mobility (UAM) scenarios using a simplified kinematic aircraft model and polynomial-based path planning methods.
